WASHINGTON — The stock market fell again Friday, marking a six-week slump. That’s bad news for investors — and bad timing for Dallas Rep. Pete Sessions and others who want to transform Social Security by creating investment accounts for workers.

Sessions, who runs the Republican congressional campaign effort, has been pushing as long as he’s been in the House to partly privatize Social Security. He has filed legislation six times — most recently a week ago — to let workers opt out of the program.

Each time, the idea has run into a buzzsaw of criticism, and fears about touching the “third rail” of American politics. Last week was no exception.

“To protect the future of Social Security for generations to come, we must propose creative solutions … and expand the options for every American’s retirement,” Sessions said.

His plan — essentially unchanged since he first proposed it in 1998 — would let workers invest their 6.2 percent share of payroll taxes. If all went well, after a few decades they would have a nest egg big enough to offset the guaranteed pension they’d given up, at less cost to taxpayers.

The downside, critics say, is this: One bear market could wipe out years of savings, putting entire generations of retirees at risk.

“Everyone agrees we need to tighten our belt,” said Sessions’ counterpart at the Democratic Congressional Campaign Committee, Rep. Steve Israel, D-N.Y. But “seniors who have paid into Social Security through a lifetime of hard work shouldn’t end up in a risky privatization scheme to gamble their retirement on Wall Street. The public has rejected this kind of Social Security privatization in the past and will again.”

Indeed, after President George W. Bush’s failed push for a similar plan early in his second term, most Republicans backed away from the idea.

“The last serious push collapsed with Bush’s popularity,” said Michael Tanner, a privatization advocate at the Cato Institute, a libertarian think tank.

He called Sessions’ legislation a great idea that has no chance of becoming law any time soon.

“On the other hand, I don’t see an alternative,” Tanner said. “It certainly doesn’t hurt to broach the subject.”

Tom McMahon, executive director of Americans United for Change — a group that fought Bush — accused Sessions of failing to learn the lessons of history. “House Republicans don’t seem to care that the American people already rejected this scheme for turning Social Security’s guaranteed benefits into a guaranteed gamble on Wall Street,” he said.

Sessions calls his proposal the Savings Account For Every American, or SAFE, Act. (Yes, there’s a letter missing in that acronym.) This time around, he’s rounded up a half dozen initial co-sponsors, half of them Texans: the party’s No. 4 House leader, Dallas Rep. Jeb Hensarling; Judiciary Committee Chairman Lamar Smith of San Antonio; and Rep. Randy Neugebauer of Lubbock.

The support from two members of GOP leadership has given Democrats an extra opening to pounce, though the House GOP budget doesn’t include a Social Security overhaul. Still, House Budget Chairman Paul Ryan, R-Wis., embraces the general approach. He included a similar plan in his “Roadmap for America’s Future,” the House GOP’s fiscal manifesto.

And while Democrats resist private accounts, Social Security did start paying out more last year than it took in.

Keeping the system solvent in the long run would require some combination of benefit cuts and tax hikes — neither of them especially popular — or some fundamental restructuring.

But private accounts are no panacea.

In the short run, they actually require more federal spending. That’s because Social Security is a pay-as-you-go system: This week’s paychecks fund next week’s retirement checks. Diverting payroll taxes creates a shortfall. Critics say the Sessions plan would divert 40 percent of the revenue, forcing Congress to find billions of dollars elsewhere to cover promised benefits during a transition that lasts several years.

“Our nation’s Social Security Trust Fund is depleting at an alarming rate,” Sessions said, “and failure to implement immediate reforms endangers the ability of Americans to plan for their retirement with the options and certainty they deserve.”